UNIT – I
Partial fraction
Introduction, Polynomial, Rational fractions, Proper and Improper fractions,
Partial fraction , Resolving into Partial fraction, Application of Partial
Fraction in Chemical Kinetics and Pharmacokinetics
Logarithms
Introduction, Definition, Theorems/Properties of logarithms, Common
logarithms, Characteristic and Mantissa, worked examples, application of
logarithm to solve pharmaceutical problems.
Function:
Real Valued function, Classification of real valued functions,
UNIT –II
Matrices and Determinant:
Introduction matrices, Types of matrices, Operation on matrices,
Transpose of a matrix, Matrix Multiplication, Determinants, Properties of
determinants , Product of determinants, Minors and co-Factors, Adjoint
or adjugate of a square matrix , Singular and non-singular matrices,
Inverse of a matrix, Solution of system of linear of equations using matrix
method, Cramer’s rule, Characteristic equation and roots of a square
matrix, Cayley–Hamilton theorem,Applicationof Matrices in solving
Pharmacokinetic equations
UNIT – III
Calculus Differentiation :
Introductions, Derivative of a function, Derivative of a
constant, Derivative of a product of a constant and a function , Derivative
of the sum or difference of two functions, Derivative of the product of two
functions (product formula), Derivative of the quotient of two functions
(Quotient formula) – Without Proof, Derivative of x
n w.r.tx,where n is any
rational number, Derivative of e
x
,, Derivative of loge x , Derivative of
a
x
,Derivative of trigonometric functions from first principles (without
Proof), Successive Differentiation, Conditions for a function to be a
maximum or a minimum at a point. Application
UNIT – IV
Analytical Geometry
Introduction:
Signs of the Coordinates, Distance formula,
Straight Line :
Slope or gradient of a straight line, Conditions for
parallelism and perpendicularity of two lines, Slope of a line joining two
points, Slope – intercept form of a straight line
Integration:
Introduction, Definition, Standard formulae, Rules of integration , Method of
substitution, Method of Partial fractions, Integration by parts, definite
integrals, application
UNIT-V
Differential Equations :
Some basic definitions, Order and degree, Equations in separable form , Homogeneous equations, Linear
Differential equations, Exact equations, Application in solving
Pharmacokinetic equations
Laplace Transform :
Introduction, Definition, Properties of Laplace
transform, Laplace Transforms of elementary functions, Inverse
Laplace transforms, Laplace transform of derivatives, Application to
solve Linear differential equations, Application in solving Chemical
kinetics and Pharmacokinetics equations
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